On at least two crucial issues, trade and the environment, Trump will be able to achieve many of his goals through his executive authority as president. On other issues, Trump will require Congress's cooperation. The obstacles might not be insurmountable, but they are substantial.
Let's take a quick look at the to-do list for Republicans:
Infrastructure was the first item Trump mentioned in his victory speech last night. Ryan has said infrastructure is no longer a priority.
For Ryan's part, addressing fiscal imbalances in the long term through reforming entitlements is a major priority. Yet Trump has said he intends to preserve Social Security and Medicare as they exist.
Trump has promised repeatedly to repeal the Affordable Care Act, President Obama's health reform, and Ryan agrees with this goal. Yet winning the election has not liberated Republicans from the difficulties of making health-care policy. Conservative Republicans might object to the health-care plan Ryan and his colleagues put forward earlier this year on the grounds that it is both costly and preserves some essential features of the current law, commonly known as Obamacare.
The GOP lawmakers' proposal would eliminate the Affordable Care Act's requirement that all individual Americans have health insurance, and it would repeal the taxes levied under the reform. However, subscribers would continue to receive generous subsidies to help pay for insurance, though the proposal did not specify how large these subsidies would be or their total cost to the federal government.
For his part, Trump has not advanced a detailed plan of his own.
From there, the issues only get trickier.
Consider immigration, which Trump used to define his candidacy. The New York businessman has called for requiring businesses around the country to electronically verify that their employees can work legally in the United States. An estimated 8 million workers are undocumented immigrants, and this kind of policy could force many of them to leave the country.
Trump, however, could confront opposition from moderate Republican lawmakers such as Ryan -- who supports granting legal status to undocumented immigrants -- and from the business lobby. Even those firms that do not rely on illegal labor would likely resent the additional paperwork.
Moreover, if Trump picks a fight on punitive immigration policy, he might have to do it without the public on his side. In a poll conducted in September by The Washington Post and ABC News, 79 percent of all those surveyed favored eventual citizenship for undocumented immigrants -- including 60 percent of Trump's own supporters, a substantial majority.
Just as the issue of immigration has defined Trump's political identity, poverty has defined Ryan's. The pair do not have any obvious disagreements when it comes to poverty, primarily because Trump has said little it.
If Ryan wants to put a bill on Trump's desk in the Oval Office, however, he would have to get it through Congress first.
The plan he and his Republican colleagues put forward earlier this year suggested there are real disagreements among conservative lawmakers about how to address the problem. That document did not take clear positions on crucial questions, such as how involved the state should be in the managing the lives of the poor.
Another issue Republicans would have to resolve is whether to focus public help on the very poor to save money, a tack that could arguably discourage work by revoking benefits for people who have somewhat more earnings. An alternative approach is to create broader and costlier programs that support more people regardless of income and that allow them to enjoy greater material rewards from their paychecks.
More from Wonkblog: